1. Field of the Invention
The present invention relates to an equivalent material constant calculation system that calculates an equivalent material constant of a structure made from a plurality of materials having different material constants, an equivalent material constant calculation program, an equivalent material constant calculation method, and a design system and manufacturing method for such a structure.
2. Description of Related Art
For example, in the design of electronic equipment, it is possible to model the electronic equipment such that the electronic equipment can be handled as data on a computer, and predict temperature, stress, and the like by performing a simulation that employs, for example, a finite element method.
When modeling electronic equipment, the shape of components that constitute the electronic equipment, the material constant, and the like are necessary as data. For example, the shape of an electronic circuit board that is a component part of the electronic equipment and the material constant (for example, thermal conductivity) are necessary as data. The electronic circuit board is configured of a wired portion made from metal material and a non-wired portion made from resin material. Thus, the electronic circuit board includes metal material and resin material, which are materials with different material constants. In this case, it is not possible to model all of the wires using a computer having present day specifications. Consequently, it is necessary to solve for an equivalent material constant by considering all or a part of the entire electronic circuit board, which is made from a plurality of materials that have different material constants, as a structure made from a plurality of materials that have one equivalent material constant.
As a method of calculating this sort of equivalent material constant, a calculation method of an equivalent thermal conductivity that takes into consideration a wiring pattern on the electronic circuit board is known, as disclosed in JP 2000-180395A. FIG. 26 is a flowchart that shows an overview of an electronic circuit board equivalent thermal conductivity calculation method, and which is an example of this conventional equivalent material constant calculation method.
In Step S911, shape data of the electronic circuit board that is the target of the equivalent thermal conductivity calculation is input. The electronic circuit board is configured by layering a wire pattern layer (hereinafter, referred to as a ‘wire layer’) and an insulation layer. As shape data, for example, data relating to various shapes is input, such as the outer contour of the entire electronic circuit board, the position and size of holes in the electronic circuit board when such holes exist, the thickness of the wire layer and the insulation layer, and the shape of the wire pattern in each wire layer.
In Step S912, material data of the electronic circuit board is input. As material data, for example, a thermal conductivity of the wire material, which is metal material that constitutes the wire pattern of the electronic circuit board, and a thermal conductivity of the insulation material, which is resin material that constitutes the insulation layer and the non-wire portion that is the portion other than the wire pattern, are input.
In Step S913, the electronic circuit board for which this equivalent thermal conductivity calculation will be performed is divided into a number N of small regions of each wire layer and insulation layer of this electronic circuit board.
In Step S914, the wire pattern surface area and the insulating portion surface area, which is the area other than the wire pattern, are obtained for each divided small region using the shape data of the electronic circuit board that was input in above Step S911, and from both of these surface areas a surface area ratio of the wire portion in each small region is calculated. Ordinarily the electronic circuit board has a very complicated shape, and reflecting this fact, the shape data of this electronic circuit board also is very complicated. However, by dividing the electronic circuit board into small regions, the shape of the wire pattern in those small regions becomes, for example, a straight line or arc, or a square or triangle, or part of a circle, or a shape that can be approximated by at least these shapes. As a result, it is possible to calculate the wire pattern surface area and the other, insulation portion surface area with relative ease and high accuracy.
In Step S915, by adding up the wire portion surface area ratio of these divided N-small regions, a wire portion surface area ratio is calculated for each wire layer or insulation layer. The formula for obtaining the wire portion surface area ratio for each of these layers is shown in formula 1. Pi in formula 1 indicates the wire portion surface area ratio of a layer No. i.
                              P          i                =                              ∑                          j              =              1                        N                    ⁢                                    p              ij                        /            N                                              Formula        ⁢                                  ⁢        1            In formula 1, Pij is the wire portion surface area ratio of a small region No. j of the layer No. i.
This formula obtains an average of the wire portion surface area ratios of each small region. However, here it is assumed that the surface area of the divided small regions is equal.
In Step S916, an equivalent thermal conductivity λp of the entire electronic circuit board that is regarded as lamination material is calculated using the wire portion surface area ratio calculated for each of the wire and insulation layers.
It is possible to use formula 2 or formula 3 for this calculation of λp. Formula 2 is a formula for a case in which the thermal conductivity effect of the insulator material is ignored. Ordinarily, the thermal conductivity of the insulator material is very small in comparison to the thermal conductivity of the wire material, and so it is possible to lighten the calculation load by ignoring the thermal conductivity effect of the insulator material as in formula 2. Formula 3 is a formula for a case in which the thermal conductivity effect of the insulator material is taken into consideration.
                                              ⁢                              λ            p                    =                                    ∑              i                        ⁢                          (                                                λ                  i                                ⁢                                  P                  i                                ⁢                                  α                  i                                            )                                                          Formula        ⁢                                  ⁢        2                                                          ⁢                                            λ              p                        =                          A              +              B                                ⁢                                          ⁢                      A            =                          ∑                                                (                                                            (                                                                                                    λ                            A                                                    ⁢                                                      P                            i                                                                          +                                                                              λ                            B                                                    ⁡                                                      (                                                          1                              -                                                              P                                i                                                                                      )                                                                                              )                                        ⁢                                          α                      i                                                        )                                ⁢                                                                  ⁢                                  (                                      ∑                                                                                  ⁢                                          is                      ⁢                                                                                          ⁢                      wire                      ⁢                                                                                          ⁢                      layer                      ⁢                                                                                          ⁢                      sum                      ⁢                                                                                          ⁢                      only                                                        )                                                              ⁢                                          ⁢                                          ⁢                      B            =                          ∑                                                (                                                            λ                      B                                        ⁢                                          α                      i                                                        )                                ⁢                                                                  ⁢                                  (                                      ∑                                                                                  ⁢                                          is                      ⁢                                                                                          ⁢                      insulation                      ⁢                                                                                          ⁢                      layer                      ⁢                                                                                          ⁢                      sum                      ⁢                                                                                          ⁢                      only                                                        )                                                                                        Formula        ⁢                                  ⁢        3            In Formula 2, λi, Pi, and αi indicate the following values:    λi: thermal conductivity of the wire material of layer No. i (W/m·K)    Pi: wire portion surface area ratio of layer No. i (0.0 for the insulation layer)    αi: ratio at which the thickness of layer No. i accounts for the thickness of the entire electronic circuit board (see Formula 4).
                                          ∑            i                    ⁢                      α            i                          =        1                            Formula        ⁢                                  ⁢        4            In formula 3, λA and λB indicate the following values. Pi and αi are the same as in formula 2.    λA: thermal conductivity of the wire material (W/m·K)    λB: thermal conductivity of the insulator material (W/m·K)
In formula 3, portions of the wire material that are included in the insulation layer (such as through holes) are ignored. If portions of the wire material that are included in the insulation layer also are considered, then it is possible to perform the calculation for B in formula 3 in the same manner as the calculation for A.
Further, in formula 3, it is assumed that the wire material of each layer and also the insulator material of each layer are the same (or at least that the thermal conductivity of the wire material of each layer is the same, and that the thermal conductivity of the insulator material of each layer is the same).
In Step S917, equivalent thermal conductivity information for the entire electronic circuit board that was calculated in Step S916 is output to a thermal conductivity database or the like. The equivalent thermal conductivity saved in the thermal conductivity database afterwards can be read and used when performing a thermal conductivity analysis that employs a finite element method or the like.
However, in the conventional equivalent material constant calculation method described above, an equivalent material constant is calculated using a surface area ratio of the occupied surface area of each electronic material (wire material and insulator material), but the directionality of the shape of the portion occupied by each electronic material on the electronic circuit board is not considered at all.
Even assuming that a particular electronic material occupies the same surface area on one board, the equivalent material constant differs greatly according to the directionality of the shape of the portion on that board that is occupied by that electronic material.
FIG. 27 shows an example of a wire pattern of an electronic circuit board. For example, in an electronic circuit board 921 shown in FIG. 27A, a wire pattern 923 constituted by wire material that is a good thermal conductor occupies a long and narrow surface area along the direction of the X axis, and six strips of that wire material are present. In this electronic circuit board 921, for example, when heat is transmitted in the direction of the X axis, the transmission of heat is good because it is transmitted from one side to the opposite side through the wire pattern 923, which is a good thermal conductor. On the other hand, when heat is transmitted in the direction of axis Y, the transmission of heat becomes poor because it is transmitted alternately through the wire pattern 923 and the non-wire portion 924. Accordingly, the equivalent thermal conductivity is comparatively high in the direction of the X axis, and comparatively low in the direction perpendicular to direction X (the direction of the Y axis).
Conversely, as in an electronic circuit board 922 shown in FIG. 27B, when the wire pattern 923, which is constituted by wire material that is a good thermal conductor, occupies a long and narrow surface area along the direction of the Y axis and is present in seven strips, the thermal conductivity becomes comparatively high in the direction of the Y axis, and comparatively low in the direction of the X axis, which is perpendicular to the Y axis.
Because the equivalent material constant that can be obtained by the conventional equivalent material constant calculation method described above is calculated using a surface area ratio of the occupied surface area, the directionality of the shape of the portion occupied by each electronic material on the electronic circuit board is not taken into consideration at all. Thus, for example, as shown in FIGS. 27A and 27B, when the shape of the portion occupied by each material is anisotropic, the calculated equivalent material constant cannot avoid an extremely large error.
As one approach for solving this problem, for example, it has been conceived to divide the electronic circuit board into even smaller regions and obtain an equivalent material constant for each of the divided small regions, thereby reducing the size of the error. However, this approach makes a greater amount of calculation time necessary. Also, because the equivalent material constant for each small region does not take into consideration the different directionality of the shape of the portion that each electronic material occupies, this method has little effectiveness for increasing the accuracy of an equivalent material constant having anisotropy. Thus, there is the problem that the effectiveness of calculation processing worsens.
Also, when the electronic circuit board is finely divided, the amount of data output as calculation results becomes large because as many equivalent material constants are output as there are divided small regions. Thus, analysis processing also becomes complicated when analysis is performed using the output equivalent material constants, and the effectiveness worsens.